Math Problem Statement

Find the y-value of the midpoint of segment AC given points A(8, 5) and C(4, -3).

Solution

To find the y-value of the midpoint of segment ACAC, we'll use the midpoint formula. Given two points A(x1,y1)A(x_1, y_1) and C(x2,y2)C(x_2, y_2), the midpoint MM is calculated as:

M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

For this problem:

  • Point AA is (8,5)(8, 5)
  • Point CC is (4,3)(4, -3)

Step 1: Substitute the coordinates into the midpoint formula:

M=(8+42,5+(3)2)M = \left( \frac{8 + 4}{2}, \frac{5 + (-3)}{2} \right)

Step 2: Calculate the x and y values separately.

  1. The x-coordinate of MM is: 8+42=122=6\frac{8 + 4}{2} = \frac{12}{2} = 6

  2. The y-coordinate of MM is: 5+(3)2=22=1\frac{5 + (-3)}{2} = \frac{2}{2} = 1

So, the midpoint MM is (6,1)(6, 1).

Answer: The y-value of the midpoint of ACAC is 1.

Would you like further details or have any questions?

Here are five related questions to explore:

  1. How would you find the distance between points AA and CC?
  2. What is the x-value of the midpoint between points AA and BB?
  3. How would the midpoint change if the coordinates of point CC were different?
  4. How can we verify that this midpoint is correct?
  5. What is the significance of the midpoint in geometry?

Tip: Always double-check the signs of your coordinates, as they can significantly affect your calculations, especially for midpoints and distances.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint Calculation

Formulas

Midpoint formula M = ((x1 + x2)/2, (y1 + y2)/2)

Theorems

Midpoint theorem

Suitable Grade Level

Grades 7-9